1. A block of mass m is accelerated across a rough surface by a force of magnitude F that is exerted at an angle φ with the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. What is the acceleration of the block?

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2. A block of mass m is accelerated across a rough surface by a force of magnitude F that is exerted at an angle φ with the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. What is coefficient of friction between the block and surface

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3. A section of hollow pipe and a solid cylinder have the same radius, mass, and length. They both rotate about their long central axes with the same angular speed. Which object has the higher rotational kinetic energy?

• the hollow pipe

4. An electric dipole is defined as a positive charge q and a negative charge -q separated by a distance 2a. For the dipole shown in Figure, find the electric field E at P due to the dipole, where P is a distance y » a from the origin.

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5. A rod of length l has a uniform positive charge per unit length λ and a total charge Q. Calculate the electric field at a point P that is located along the long axis of the rod and a distance a from one end.

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6. A point charge q is located at a distance l from an infinite conducting plane. Determine the surface density of charges induced on the plane as a function of separation r from the base of the perpendicular drown to the plane from the charge.

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7. A thin infinitely long thread carrying a charge λ per unit length is oriented parallel to the infinite conducting plane. The distance between the thread and the plane is equal to l. Find: a) the modulus of the vector of the force acting on a unit length of the thread; b) the distribution of surface charge density σ(x) over the plane, where x is the distance from the plane perpendicular to the conducting surface and passing through the thread.

• ,

8. A thin wire ring of radius R carries a charge q. Find the magnitude of the electric field strength on the axis of the ring as a function of distance l from its centre.

• 

9. At 25.0 m below the surface of the sea (ρ= 1 025 kg/m³), where the temperature is 5.00°C, a diver exhales an air bubble having a volume of 1.00 cm³. If the surface temperature of the sea is 20.0°C, what is the volume of the bubble just before it breaks the surface? (P₀= 1.013* 10⁵ Pa).

• 3.67 cm³

10. An aluminum cup of mass 200 g contains 800 g of water in thermal equilibrium at 80.0°C. The combination of cup and water is cooled uniformly so that the temperature decreases by 1.50°C per minute. At what rate is energy being removed by heat? Express your answer in watts. (Specific heat of aluminium and water c_al =900 J/kg ^. °C, c_w =4186 J/kg ^. °C).

• 88.2 W

11. A sample of ideal gas is expanded to twice its original volume of 1.00 m³ in a quasi-static process for which P= αV², α=5.00 atm/m⁶, as shown in Figure. How much work is done on the expanding gas? (1 atm= 1.013* 10⁵ Pa).

• - 1.18 MJ

12. A sample of an ideal gas is in a vertical cylinder fitted with a piston. As 5.79 kJ of energy is transferred to the gas by heat to raise its temperature, the weight on the piston is adjusted so that the state of the gas changes from point A to point B along the semicircle shown in Figure. Find the change in internal energy of the gas.

• 3.6 kJ

13. A multicylinder gasoline engine in an airplane, operating at 2 500 rev/min, takes in energy 7.89 * 10³ J and exhausts 4.58 *10³ J for each revolution of the crankshaft. How many liters of fuel does it consume in 1.00 h of operation if the heat of combustion is 4.03 * 107 J/L?

• 29.4 l/h

14. A plane loop of wire consisting of a single turn of cross-sectional area 100 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.5 T to 2.5 T in a time of 1.5 s. What is the resulting induced current if the coil has a total resistance of 4 Ω?

• 3A

15. A 20-turn circular coil of radius 5 cm and resistance 0.5 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.02t + 0.05t², where t is in s and B is in T. Calculate the induced emf in the coil at t = 6 s.

• 97.4 mV

16. A body is moving parallel to the z-axes. Its velocity is constant and equal to 12 m/s. Which vector of velocity is possible:

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17. A body moves along the y-axes. When the velocity is positive? (more than one answer can be right)

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• 

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18. A baseball of mass m is thrown upward with some initial speed. A gravitational force is exerted on the ball

• At all points in its motion

19. A mechanical wave generally does NOT

• move the medium from one place to another

20. A skater can spin faster by pulling in her arms closer to her body or spin slower by spreading her arms out from her body. This is due to

• Conservation of angular momentum

21. A conductor in electrostatic equilibrium has the following properties:

• 1. The electric field is zero everywhere inside the conductor. 2. Any net charge on the conductor resides entirely on its surface. 3. The electric field just outside the conductor is perpendicular to its surface and has a magnitude σ/ε₀, where σ is the surface charge density at that point. 4. On an irregularly shaped conductor, the surface charge density is greatest where the radius of curvature of the surface is the smallest.

22. A helium-filled rubber balloon is left in a car on a cold winter night. Compared to its size when it was in the warm car the afternoon before, the size the next morning is

• Smaller

23. Adiabatic process is

• process in which the net heat transfer between the system and its surroundings is zero

24. A diatomic gas molecule has ... degrees of freedom

• 6

25. A material that can be permanently magnetized is generally said to be

• ferromagnetic

26. A device that reverses magnetic field polarity to keep a dc motor rotating is

• a commutator

27. A coil of wire is placed in a changing magnetic field. If the number of turns in the coil is decreased, the voltage induced across the coil will

• decrease

28. A conductor in electrostatic equilibrium has the following properties:

• 1. The electric field is zero everywhere inside the conductor. 2. Any net charge on the conductor resides entirely on its surface. 3. The electric field just outside the conductor is perpendicular to its surface and has a magnitude σ/ε₀, where σ is the surface charge density at that point. 4. On an irregularly shaped conductor, the surface charge density is greatest where the radius of curvature of the surface is the smallest.

29. A parallel-plate capacitor with air between the plates has an area A=2.00·10⁴ m² and a plate separation d=1.00 mm. Find its capacitance.

• C=1.77 pF

30. A parallel-plate capacitor has plates of dimensions 2.0 cm by 3.0 cm separated by a 1.0-mm thickness of paper. Find its capacitance (k = 3.7, ε₀=8.85·10^-12 C²/N·m²).

• 20 pF

31. An electric heater is constructed by applying a potential difference of 120 V to a Nichrome wire that has a total resistance of 8.00 Ω. Find the current carried by the wire.

• 15 A

32. An electric heater is constructed by applying a potential difference of 120 V to a Nichrome wire that has a total resistance of 8.00 Ω. Find the power rating of the heater.

• 1.8 kW

33. A battery has an emf of 12.0 V and an internal resistance of 0.05 Ω. Its terminals are connected to a load resistance of 3.00 Ω. Find the terminal voltage of the battery.

• 11.8 V

34. A single-loop circuit contains two resistors and two batteries, as shown in Figure. (Neglect the internal resistances of the batteries.) Find the current

in the circuit.

• I=-0.33 A

35. An electric dipole is defined as a positive charge q and a negative charge -q separated by a distance 2a. For the dipole shown in Figure, find the electric field E at P due to the dipole, where P is a distance y » a from the origin.

36. A rod of length l has a uniform positive charge per unit length λ and a total charge Q. Calculate the electric field at a point P that is located along the long axis of the rod and a distance a from one end.

37. A point charge q is located at a distance l from an infinite conducting plane. Determine the surface density of charges induced on the plane as a function of separation r from the base of the perpendicular drown to the plane from the charge.

38. A thin infinitely long thread carrying a charge λ per unit length is oriented parallel to the infinite conducting plane. The distance between the thread and the plane is equal to l. Find: a) the modulus of the vector of the force acting on a unit length of the thread; b) the distribution of surface charge density σ(x) over the plane, where x is the distance from the plane perpendicular to the conducting surface and passing through the thread.

• ,

39. A thin wire ring of radius R carries a charge q. Find the magnitude of the electric field strength on the axis of the ring as a function of distance l from its centre.

40. A ball is thrown upward. While the ball is in free fall, does its acceleration

• Remain constant

41. After a ball is thrown upward and is in the air, its speed in all path

• Decreases and then increases

42. A car moves along y-axes. In the figure, velocity of the car as a function of time is shown in three parts (I, II, III). Which statement is ALWAYS true?

• Velocity is constant in part II

43. A force of 3N acts perpendicularly to a force of 4N. Their resultant has magnitude of ______

• 5N

44. A man does the work if he ___________.

• Goes to fifth floor of the building

45. A sound wave can be characterized as

• A longitudinal wave

46. A woman sits on a spinning stool with her arms folded. When she extends her arms, which of the following occurs

• She increases her moment of inertia, thus decreasing her angular speed.

47. A parallel-plate capacitor with air between the plates has an area A=2.00·10⁴ m² and a plate separation d=1.00 mm. Find its capacitance.

• C=1.77 pF

48. A parallel-plate capacitor has plates of dimensions 2.0 cm by 3.0 cm separated by a 1.0-mm thickness of paper. Find its capacitance (k = 3.7, ε₀=8.85·10^-12 C²/N·m²).

• 20 pF

49. An electric heater is constructed by applying a potential difference of 120 V to a Nichrome wire that has a total resistance of 8.00 Ω. Find the current carried by the wire.

• 15 A

50. An electric heater is constructed by applying a potential difference of 120 V to a Nichrome wire that has a total resistance of 8.00 Ω. Find the power rating of the heater.

• 1.8 kW

51. A battery has an emf of 12.0 V and an internal resistance of 0.05 Ω. Its terminals are connected to a load resistance of 3.00 Ω. Find the terminal voltage of the battery.

• 11.8 V

52. A single-loop circuit contains two resistors and two batteries, as shown in Figure. (Neglect the internal resistances of the batteries.) Find the current in the circuit.

• I=-0.33 A

53. A segment of steel railroad track has a length of 30.000 m when the temperature is 0.0°C. What is its length when the temperature is 40.0°C? (Average linear expansion coefficient for steel is α=11* 10^-6 °C^-1).

• 30.013 m.

54. An ideal gas occupies a volume of 100 cm³ at 20°C and 100 Pa. Find the number of moles of gas in the container (Universal gas constant R= 8.314 J/mol*K).

• 4.11 * 10^-6 mol

55. A 50.0-g sample of copper is at 25.0°C. If 1 200 J of energy is added to it by heat, what is the final temperature of the copper? (Specific heat of copper c= 387 J/kg ^. °C).

• 87°C

56. A gas is taken through the cyclic process described in Figure. Find the net energy transferred to the system by heat during one complete cycle.

• 12 kJ

57. An ideal gas initially at 300 K undergoes an isobaric expansion at 2.50 kPa. If the volume increases from 1.00 m³ to and 12.5 kJ is transferred to the gas by heat, what is the change in its internal energy?

• 7.5 kJ

58. A glass window pane has an area of 3.00 m² and a thickness of 0.600 cm. If the temperature difference between its faces is 25.0°C, what is the rate of energy transfer by conduction through the window? (Thermal conductivity of glass k= 0.8 W/m* °C)

• 10 kW

59. A cylinder contains a mixture of helium and argon gas in equilibrium at 150°C. What is the average kinetic energy for each type of gas molecule? (Boltzmann constant k_B= 1.38* 10^-23 J/K).

• 8.76* 10^-21 J

60. A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. What is the final pressure of the gas?

• 1.39 atm

61. A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. What are the initial and final temperatures? (Universal gas constant R= 8.314 J/mol*K, 1 atm= 1.013* 10⁵ Pa )

• 365 K, 253 K

62. A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. Find Q, ΔE_int, and W (Universal gas constant R= 8.314 J/mol*K).

• 0 J, -4.66 kJ, - 4.66 kJ

63. A heat engine takes in 360 J of energy from a hot reservoir and performs 25.0 J of work in each cycle. Find the efficiency of the engine.

• 6.94 %

64. A heat engine performs 200 J of work in each cycle and has an efficiency of 30.0%. For each cycle, how much energy is (a) taken in and (b) expelled by heat?

• 667 J, 467 J

65. A particular heat engine has a useful power output of 5.00 kW and an efficiency of 25.0%. The engine expels 8 000 J of exhaust energy in each cycle. Find the energy taken in during each cycle

• 10.7 kJ

66. A rectangular copper strip 1.5 cm wide and 0.1 cm thick carries a current of 5 A. A 1.2 T magnetic field is applied perpendicular to the strip. Find the Hall voltage that should be produced.

• 0.442 µV

67. An ac voltage is applied directly across an 8 µF capacitor. The frequency of the source is 3 kHz, and the voltage amplitude is 30V. Find the voltage across the capacitor in terms of time.

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67. An ac voltage is applied directly across an 8 µF capacitor. The frequency of the source is 3 kHz, and the voltage amplitude is 30V. Find the displacement current between the plates of the capacitor.

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68. A toroidal winding carrying a current of 5 A is wound with 300 turns/m of wire. The core is iron, which has a magnetic permeability of 5000µ₀ under the given conditions. Find H inside the iron core.

• 1500

69. A toroidal winding carrying a current of 5 A is wound with 300 turns/m of wire. The core is iron, which has a magnetic permeability of 5000µ₀ under the given conditions. Find B inside the iron core.

• 9.43 T

70. Assume that a motor having coils with a resistance of 10 Ω is supplied by a voltage of 120 V. When the motor is running at its maximum speed, the back emf is 70V. Find the current in the coils when the motor is first turned on.

• 12 A

71. Assume that a motor having coils with a resistance of 10 Ω is supplied by a voltage of 120 V. When the motor is running at its maximum speed, the back emf is 70 V. Find the current in the coils when the motor has reached maximum speed.

• 5 A

72. A wire of area 2 mm² carries a current of 0.4mA. The average current density is

• 200 A/m²

73. A square loop of side 0.1m carries 2A current. The magnetic dipole moment of the loop is

• 2*10^-2 Am²

74. A toaster is rated at 600W when connected to a 120V source. What current does the toaster carry?

• 5A

75. An electrton traveling with speed v around a circle of radius r is equivalent to a current of:

• ev/2πr

76. An electromagnetic field propagates in +x direction. The electric field at a point in space is momentarily oriented in –z direction. The magnetic field at that point is momentarily oriented in

• –y direction

77. Consider a graphical representation (Fig.) of simple harmonic motion as described mathematically by equation . When the particle is at point A on the graph, what can you say about its position and velocity?

• The position is negative, and the velocity is positive

78. Consider three point charges located at the corners of a right triangle as shown in Figure, where q₁ = q₃ = 5.0 μC, q₂ =-2.0 μC, and a = 0.10 m. Find the resultant force exerted on q₃.

• F₃=(-1.1i+7.9j)N

79. Calculate the ratio of the electrostatic to gravitational interaction forces between two electrons, between two protons. At what value of the specific charge q/m of a particle would these forces become equal (in their absolute values) in the case of interaction of identical particles? (γ=6.67·10^-11 m³/(kg·s²), m_e=9·10^-31kg, m_p=1·10^-27kg, k_e=8.99·10⁹ N·m²/ C²)

• 4·10⁴² (for electrons); 1·10³⁶ (for proton); q/m=0.86·10^-10 C/kg

80. Centripetal acceleration and tangential acceleration are always __________.

• Perpendicular to each other

81. Circuits involving more than one loop are conveniently analyzed with the use of Kirchhoff’s rules:

• 1. The sum of the currents entering any junction in an electric circuit must equal the sum of the currents leaving that junction. 2. The sum of the potential differences across all elements around any circuit loop must be zero.

82. Can you create electricity with a magnet?

• Yes, by moving a wire through a magnetic field

83. Circuits involving more than one loop are conveniently analyzed with the use of Kirchhoff’s rules:

• 1. The sum of the currents entering any junction in an electric circuit must equal the sum of the currents leaving that junction. 2. The sum of the potential differences across all elements around any circuit loop must be zero.

84. Calculate the resistance of an aluminum cylinder that has a length of 10.0 cm and a cross-sectional area of 2.00·10^-4 m² (ρ=2.82·10^-8 Ω·m).

• R=1.4·10^-5 Ω

85. Calculate the resistance of an glass cylinder that has a length of 10.0 cm and a cross-sectional area of 2.00·10^-4 m² (ρ=3·10¹⁰ Ω·m).

• R=1.5·10¹³ Ω